Abstract:
We call a foliation $(M, F)$ on a manifold $M$ chaotic if it is topologically transitive and the union of closed leaves is dense in $M$. The chaotic topological foliations of arbitrary codimension on $n$-dimensional manifold can be considered as multidimensional generalization of chaotic dynamical systems in the sense of Devaney. For topological foliations covered by fibrations we prove that a foliation is chaotic if and only if its global holonomy group is chaotic. Applying the method of suspension, a new countable family of pairwise non isomorphic chaotic topological foliations of codimension two on $3$-dimensional closed and non closed manifolds is constructed.
Keywords:foliation, chaotic foliation, suspended foliation, global holonomy group.